How to find the horizontal asymptote of a rational function

Asked by admin @ 25/11/2021 in Mathematics viewed by 275 People

State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal asymptote. (5 points)

f(x)= x^2+3x-2/x-2

Answered by admin @ 25/11/2021

So here are the rules of horizontal asymptotes:

Degree of Numerator > Degree of Denominator: No horizontal asymptote
Degree of Numerator = Degree of Denominator: $y=\frac{\textsf{leading coefficient of numerator}}{\textsf{leading coefficient of denominator}}$
Degree of Numerator < Degree of Denominator: y = 0

Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that this function has no horizontal asymptote.

Give an example of a rational function that has a horizontal asymptote of y = 2/9..

Asked by maham237 @ 29/11/2020 in Mathematics viewed by 327 persons

How to find the end behavior of a rational function

Asked by admin @ 05/11/2021 in Mathematics viewed by 286 persons

State the domain and end behavior of each rational function. Identify all horizontal and vertical asymptotes on the graph of each rational function. Then, verify your answer by graphing the …

Which function has a horizontal asymptote of y 3

Asked by maham237 @ 25/04/2021 in Mathematics viewed by 295 persons

f(x) = 3(2^x) f(x) = 2(4)^x–3 f(x) = 2(3^x) f(x) = 2(4^x) + 3

Which function has no horizontal asymptote?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 277 persons

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How to find x and y intercepts of rational functions

Asked by admin @ 27/11/2021 in Mathematics viewed by 328 persons

How do we find x-intercept of rational function

Finding the x and y intercepts of a rational function

Asked by admin @ 22/11/2021 in Mathematics viewed by 342 persons

Task 3—Graphing Rational Functions Create a rational function with a linear binomial in both the numerator and denominator. -Part 1. Graph your function using technology. Include the horizontal and vertical …

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Asked by maham237 @ 12/01/2021 in Mathematics viewed by 283 persons

Find an exponential function with a horizontal asymptote y equals=2 whose graph contains the points (0,3) and (1,6).

How to find y intercept of rational function

Asked by maham237 @ 07/01/2021 in Mathematics viewed by 305 persons

PLEASE HELP!! Find the y-intercept of the rational function. A rational function is graphed in the first quadrant, and in the second, third and fourth quadrants are other pieces of …

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Asked by admin @ 04/12/2021 in Mathematics viewed by 356 persons

Find the derivative of the following function using the limit process

Find average rate of change of function over given interval

Asked by admin @ 02/12/2021 in Mathematics viewed by 325 persons

Calculate the average rate of change over the interval [1, 3] for the following function. F(x)=4(5)^x

How to find end behavior of a function without graphing

Asked by admin @ 01/12/2021 in Mathematics viewed by 310 persons

Without graphing, describe the end behavior of the graph of the function. (Image provided includes function and answer options) *Please show all work, thanks.*